Proof-code: x21

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Samuel Yates began, and this site continues, a database of the largest known primes. Primes in that database are assigned a proof-code to show who should be credited with the discovery as well as what programs and projects they used. (Discoverers have one prover-entry, but may have many proof-codes because they use a variety of programs...)

This page provides data on x21, one of those codes.

Code name (*):x21   (See the descriptive data below.)
Persons (*):2 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Broadhurst, Walker
Number of primes:total 3
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 31.5209

Descriptive Data: (report abuse)
This code is used for proofs of generalized Lucas numbers and their primitive parts. The following software was used: (1) Pari-GP for cyclotomic (and, where appropriate, Aurifeuillian) factorizations of N^2-1. (2) GMP-ECM and SIQS for extracting PrP factors of such cyclotomic cofactors. (3) Primo and VFYPR for proving these helpers prime. (4) OpenPFGW for BLS tests with these prime helpers. (5) Pari-GP for Williams-Lenstra proofs, since BLS was insufficient. The distinctive contribution of Andrew Walker was to identify the PrP targets.
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Below is additional information about this entry.

Display (text):Broadhurst, Walker
Display (short):Broadhurst & Walker
Database id:345 (do not use this database id, it is subject to change)
Proof program:unknown
Entry last modified:2024-04-19 14:37:11
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